The undirected power graph P (Z_(n) ) of a finite group Z_(n) is the graph with vertex set G and two distinct vertices u and v are adjacent if and only if u ≠ v and or . The Wiener index W (P (Z_(n) )) of an undirected power graph P (Z_(n) ) is defined to be sum of distances between all unordered pair of vertices in P (Z_(n) ). Similarly, the edge-Wiener index W_(e) (P (Z_(n) )) of P (Z_(n) ) is defined to be the sum of distances between all unordered pairs of edges in P (Z_(n) ). In this paper, we concentrate on the wiener index of a power graph , P (Z_(pq) ) and P (Z_(p) ). Firstly, we obtain new results on the wiener index and edge-wiener index of power graph P (Z_(n) ), using m,n and Euler function. Also, we obtain an equivalence between the edge-wiener index and wiener index of a power graph of Z_(n) .
展开▼
